Question

6£®aa¡ä¡¢bb¡ä¡¢cc¡äΪ×ã¹»³¤µÄÔÈÇ¿´Å³¡·Ö½çÏߣ¬ÏàÁÚÁ½·Ö½çÏß¼ä¾à¾ùΪd£¬´Å³¡·½ÏòÈçͼËùʾ£¬¢ñ¡¢¢òÇø´Å³¡¸ÐӦǿ¶È·Ö±ðΪBºÍ2B£¬±ß½çaa¡äÉÏÓÐÒ»Á£×ÓÔ´P£¬Æ½ÐÐÓÚÖ½ÃæÏò¸÷¸ö·½Ïò·¢ÉäËÙÂÊΪ$\frac{2Bqd}{m}$µÄ´øÕýµçÁ£×Ó£¬QΪ±ß½çbb¡äÉÏÒ»µã£¬PQÁ¬ÏßÓë´Å³¡±ß½ç´¹Ö±£¬ÒÑÖªÁ£×ÓÖÊÁ¿m£¬µçÁ¿Îªq£¬²»¼ÆÁ£×ÓÖØÁ¦ºÍÁ£×Ó¼äÏ໥×÷ÓÃÁ¦£¬Çó£º
£¨1£©ÑØPQ·½Ïò·¢ÉäµÄÁ£×ӷɳö¢ñÇøʱ¾­¹ýbb¡äµÄλÖã»
£¨2£©Á£×ÓµÚÒ»´Îͨ¹ý±ß½çbb¡äµÄλÖ÷¶Î§£»
£¨3£©½øÈë¢òÇøµÄÁ£×ÓµÚÒ»´ÎÔڴų¡¢òÇøÖÐÔ˶¯µÄ×ʱ¼äºÍ×î¶Ìʱ¼ä£®

Answer 1

·ÖÎö £¨1£©ÓÉÂåÂØ×ÈÁ¦ÌṩÏòÐÄÁ¦ºÍÌâÉèÌõ¼þÇóµÃ°ë¾¶£¬Ô²ÐÄÔÚPµãÕýÏ·½£¬ÓÉÓɼ¸ºÎ¹Øϵ¾ÍÄÜÇó³öÑØˮƽ·½ÏòÉä³öºóÏòÏÂÆ«ÀëµÄ¾àÀ룮
£¨2£©ÓÉÓÚÁ£×ÓµÄËٶȷ½Ïò²»¶¨£¬µ«°ë¾¶Ò»¶¨£®¸ù¾ÝÁ£×ÓÐýתµÄ·½Ïò£¨ÔÚ¢ñÇø˳ʱÕ룬ÔÚ¢òÇøÄæʱÕ룩ÏÈÈ·¶¨ÏòÉÏ´òµ½µÄ×î¸ßµã£¬¼´ÑØ×ÅÊúÖ±ÏòÉÏ·½ÏòÉä³öµÄÁ£×Ó£¬¾Ý´ËÓɼ¸ºÎ¹ØϵÇó³ö×î¸ßµãÆ«ÀëPµãµÄ¾àÀ룻ÔÙÈ·¶¨×îµÍµã£¬ÏÔÈ»µ±¹ì¼£Óëbb¡äÏàÇÐʱ£¬¸ÃµãΪ×îµÍµã£®
£¨3£©ÒªÊ¹Á£×ÓÔÚ¢òÇøÔ˶¯µÄʱ¼ä×ºÍ×î¶Ì£¬ÔòÒªÇóÔÚ¸ÃÇø×öÔ²ÖÜÔ˶¯µÄÏÒ³¤×ºÍ×î¶Ì£¬ÓɴŸÐӦǿ¶ÈµÄ¹ØϵÇó³öÔÚ¸ÃÇø×öÔ²ÖÜÔ˶¯µÄ°ë¾¶£®´Ó¶øÇó³ö×ºÍ×î¶ÌµÄʱ¼ä£®

½â´ð ½â£º£¨1£©ÓÉÂåÂ××ÈÁ¦³äµ±ÏòÐÄÁ¦µÃ£º
   $qvB=\frac{m{v}^{2}}{R}$             
   $R=\frac{mv}{qB}$               
  °Ñ$v=\frac{2Bqd}{m}$´úÈëµÃr₁=2d
  ÈçͼËùʾ¿ÉµÃ£º
   $sin¦È=\frac{d}{2d}=\frac{1}{2}$
   ¦È=30¡ã
   $PM=QN=2d-2dcos¦È=£¨2-\sqrt{3}£©d$          
  ËùÒÔ£¬¾­¹ýbb¡äµÄλÖÃΪQÏ·½$£¨2-\sqrt{3}£©d$
£¨2£©µ±ÕýµçÁ£×ÓËÙ¶ÈÊúÖ±ÏòÉϽøÈë´Å³¡¢ñ£¬¾àÀëQµãÉÏ·½×îÔ¶£º
  Óɼ¸ºÎ¹ØϵµÃ£º$cos{¦Á}_{1}=\frac{d}{2d}=\frac{1}{2}$
   ¦Á₁=60¡ã
  $Q{H}_{1}=2dsin{¦Á}_{1}=\sqrt{3}d$      
  µ±ÕýµçÁ£×Ó½øÈëºóÓëbb¡äÏàÇÐʱ£¬¾àÀëQµãÏ·½×îÔ¶£º
  Óɼ¸ºÎ¹ØϵµÃ£º$cos{¦Á}_{2}=\frac{d}{2d}=\frac{1}{2}$
  ¦Á₂=60¡ã
  $Q{H}_{2}=2dsin{¦Á}_{2}=\sqrt{3}d$         
  ËùÒÔÓÐÁ£×Óͨ¹ýµÄ·¶Î§³¤¶ÈΪ$L=2\sqrt{3}d$
£¨3£©Í¬Àí£ºÔڴų¡¢òÖеİ뾶£º${r}_{2}=\frac{mv}{q{B}_{2}}=d$        
 ÖÜÆÚ£º$T=\frac{2¦ÐR}{v}=\frac{¦Ðm}{qB}$           
  ¹ì¼£Ô²Ëù¶ÔÓ¦µÄÏÒÔ½³¤£¬Ôڴų¡¢òÖеÄʱ¼äÔ½³¤£®
  µ±¹ì¼£Ô²µÄÏÒ³¤ÎªÖ±¾¶Ê±£¬Ëù¶ÔÓ¦µÄʱ¼ä×Ϊ£º
  ${t}_{max}=\frac{T}{2}=\frac{¦Ðm}{2qB}$          
  µ±¹ì¼£Ô²µÄÏÒ³¤Îª´Å³¡¢òµÄ¿í¶Èʱ£¬´Ócc¨@·É³öËù¶ÔÓ¦µÄʱ¼ä×î¶ÌΪ£º
   ${t}_{min}=\frac{T}{6}=\frac{¦Ðm}{6qB}$
  ´Óbb¨@·É³öËù¶ÔÓ¦µÄʱ¼ä×î¶ÌΪ${t_{min}}=\frac{T}{3}=\frac{¦Ðm}{3qB}$
  ËùÒÔ£º×î¶Ìʱ¼äΪ${t_{min}}=\frac{¦Ðm}{6qB}$
´ð£º£¨1£©ÑØPQ·½Ïò·¢ÉäµÄÁ£×ӷɳö¢ñÇøʱ¾­¹ýbb¡äµÄλÖÃΪQÏ·½$£¨2-\sqrt{3}£©d$£®
£¨2£©Á£×ÓµÚÒ»´Îͨ¹ý±ß½çbb¡äµÄλÖ÷¶Î§Îª$2\sqrt{3}d$£®
£¨3£©½øÈë¢òÇøµÄÁ£×ÓµÚÒ»´ÎÔڴų¡¢òÇøÖÐÔ˶¯µÄ×ʱ¼äΪ$\frac{¦Ðm}{2qB}$¡¢×î¶Ìʱ¼äΪ$\frac{¦Ðm}{6qB}$£®

µãÆÀ ±¾ÌâµÄö¦µãÔÚÓÚµÚ¶þ¡¢ÈýÎÊ£º¢ÙÁ£×ÓµÄËٶȴóСһ¶¨£¬µ«·½Ïò²»Í¬£¬ÔÚ¿¼ÂÇ´òÔÚbb¡ä×î¸ßºÍ×îµÍλÖÃʱ£¬ÏÈҪȷ¶¨Á£×ÓÐýתµÄ·½Ïò£¬»¹Ðè±È½Ï°ë¾¶Óë¿í¶ÈµÄ¹Øϵ£¬²ÅÄÜÕÒµ½ÕýÈ·´ð°¸£¬ÔÙÓɼ¸ºÎ¹ØϵÇó³ö´òÔÚbb¡äÉϵķ¶Î§£®¢ÚÓÉÓÚÔÚ¢òÇø×öÔÈËÙÔ²ÖÜÔ˶¯µÄ°ë¾¶²»Í¬£¬Çó×ʱ¼äʱ£¬Ò²ÒªÏÈÈ·¶¨Á£×ÓµÄÐýת·½Ïò¡¢¿í¶ÈÓë°ë¾¶µÄ¹Øϵ£ºµ±¹ì¼£Ô²µÄÏÒ³¤ÎªÖ±¾¶Ê±£¬Ëù¶ÔÓ¦µÄʱ¼ä×£» µ±¹ì¼£Ô²µÄÏÒ³¤Îª´Å³¡¢òµÄ¿í¶Èʱ£¬´Ócc¨@·É³öËù¶ÔÓ¦µÄʱ¼ä×î¶Ì£®